%%
%% fourierIndex.tex
%% 
%% Made by Alex Nelson
%% Login   <alex@tomato>
%% 
%% Started on  Fri Dec 19 22:15:05 2008 Alex Nelson
%% Last update Sat Jan  3 15:42:05 2009 Alex Nelson
%%
%% TODO: I need to do some more work on Fourier transforms 
%%
\part{Fourier Series}
\section{Differential Equations: A Motivation for Fourier Series}
\input{tex/31March2008}
\section{A First Look at Fourier Series}
\input{tex/2April2008}
\section{Bessel's Inequality}
\input{tex/4April2008}
%% Convergence of series, pointwise convergence?
\section[Convergence, Termwise Calculus]{Convergence of Fourier Series, Termwise Integration and Differentiation}
\input{tex/9April2008}
\section[Decay of Coefficients, Arbitrary Intervals]{Smoothness and Decay of Fourier Coefficients, Fourier Expansion on Arbitrary Intervals}
\input{tex/11April2008}
\section{A Review of Vector Spaces}\index{Vector Space}
\input{tex/reviewVectorSpace}
\input{tex/16April2008}
\section{$L^{2}$ spaces}
\input{tex/18April2008}
\section{Orthonormal Basis for $L^2$}
\input{tex/21April2008}
\section{More on Orthonormal Basis, Spectral Theorem}
\input{tex/23April2008}
\section{The Regular Sturm-Liouville Problem}
\input{tex/25April2008}
\section{Properties of Weighted Inner Products}
\input{tex/28April2008}
\section{Solving the Heat Equation using Sturm-Liouville Problem}
\input{tex/30April2008}
\section{Using Fourier Series to Solve the Heat Equation}
\input{tex/2May2008}
%%%%
%%    Fourier Transform
%%%%
\part{Fourier Transforms}
\section{A Review of $L^{2}$ and an Introduction to the Fourier Transform}
\input{tex/5May2008}
\section{Convolution}
\input{tex/9May2008}
\input{tex/12May2008}
\section{Examples and Basic Properties of Fourier Transform}
\input{tex/14May2008}
\section{Inverse Fourier Transform, Fourier Transform on $L^2$}
\input{tex/16May2008}
\input{tex/19May2008part1}
\part{Discrete Fourier Transforms}
\section{Sampling Theorem}
\input{tex/21May2008}
\section{Uncertainty Principle}
\input{tex/23May2008}
%\input{tex/28May2008}
%\input{tex/30May2008}
%\input{tex/2June2008}
%\input{tex/6June2008}
\nocite{morseVolOne}
\nocite{textbook}
